Show commands:
SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 68400gm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68400.u1 | 68400gm1 | \([0, 0, 0, -17625, -610625]\) | \(132893440/41553\) | \(189325856250000\) | \([]\) | \(161280\) | \(1.4438\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68400gm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 68400gm do not have complex multiplication.Modular form 68400.2.a.gm
sage: E.q_eigenform(10)